Increased computing power and the Web have made information widely accessible. In turn, this has encouraged the development of recommendation systems that help users find items of interest, such as books or restaurants. Such systems are more useful when they personalize themselves to each user's preferences, thus making the recommendation process more efficient and effective. In this paper, we present a new approach to recommendation systems: that of personalized conversational recommendation. This system uses the complementary strengths of recommendation systems and dialogue systems to overcome their respective deficiencies. We present a system -- the Adaptive Place Advisor -- implementing our ideas. This system treats item selection as an interactive, conversational process, with the program inquiring about item attributes and the user responding. The system incorporates a user model that contains item, attribute, and value preferences, which it updates during each conversation and maintains across sessions. The Place Advisor utilizes both the conversational context and the user model to retrieve candidate items from a database. It uses personalized heuristics to select which attribute to ask about in order to narrow down and rank possible choices. We report experimental results demonstrating the effectiveness of user modeling in reducing the time and number of interactions required to find a satisfactory item.